Approximation Properties of a Gradient Recovery Operator Using a Biorthogonal System

TL;DR

This paper investigates a gradient recovery operator using biorthogonal systems, analyzing its approximation capabilities and computational efficiency within finite element methods.

Contribution

It introduces a gradient recovery operator based on oblique projection with biorthogonal bases, enhancing computational efficiency and approximation analysis.

Findings

Efficient computation of the recovery operator due to biorthogonality

Analysis of the approximation properties of the operator

Potential improvements in finite element gradient recovery methods

Abstract

A gradient recovery operator based on projecting the discrete gradient onto the standard finite element space is considered. We use an oblique projection, where the test and trial spaces are different, and the bases of these two spaces form a biorthogonal system. Biorthogonality allows efficient computation of the recovery operator.We analyse the approximation properties of the gradient recovery operator.